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A new methodology for long-term planning over large transmission systems is proposed. It aims at finding the optimal design of a large grid including its modular development plan over a long-time horizon. Advanced optimization and simulation methods have been investigated to tackle this complex problem which includes highly combinatorial aspects and stochastic behaviours of system components, while ensuring some control over the system.

An estimation of the computationl resources needed for a real study over a system of the size of the whole pan-European network for the 2020 to 2050 period is given based on a case study for the French and Spanish systems.

**Challenge:** **How to address long-term planning over large transmission systems, taking into account all time and spatial scales within a probabilistic approach?**

Long-term planning over large transmission systems, such as the European transmission network, is a complex problem. Indeed transmission planning is usually performed for time horizons comprised between 10 to 20 years and so far current planning methodologies have not coped with planning over large areas and with increased uncertainty (significant shares of renewable energy such as wind and solar). Although several studies have addressed these topics [1], as of today, national transmission systems in Europe are planned by resorting to expert views. The e-Highway2050 project aims precisely at defining a new methodology and developing associated tools where long-term planning is formalised as an optimisation problem, seen from the transmission operator’s perspective with no control over generation planning: several possible evolutions of the electricity sector are investigated for different energy scenarios . The main challenges arise from the multi-scale and stochastic features of the problem: methods to reduce the size of the grid and to choose relevant snapshots among the 8760 hours of a year have been developed. The process followed by the developed methodology is represented in Figure 1.

Generation and consumption are first generated with an hourly time step for a set of areas of the modelled power system to ensure system adequacy for each scenario and each time horizon, with several patterns of uncertainty and no grid constraints (copper plate). Overload problems are then detected on a simplified initial pan-European nodal grid (around 1,000 nodes). In a third step, the initial network is reduced according to critical branches, leading to a zonal initial grid (100 nodes). The modular development plan is then calculated at the zonal level considering all time horizons and the whole set of scenarios (step 4). Starting from the zonal modular development plan, a grid expansion is performed for the first two time horizons (2020 and 2030) at a nodal level. Finally, the robustness of the nodal grid architectures is checked to ensure that these grids can be operated without major voltage or grid stability issues.

The operation of the electrical system in “copperplate” is first simulated: balanced Time Series (TS) of consumption and generation for different patterns of uncertainty are generated. These TS are then used in the following steps as reference injections constituting a base to design the future network expansions.

A Monte Carlo approach is used to create times series (TS) for generation (wind and solar power generation, hydro inflows and outages of thermal units) and load at an hourly time step, over a period of one year and for each area of the modelled power system. It mimics the intrinsic characteristics observed in past realizations, notably seasonality, autocorrelation, probability density function and cross-correlation, and assumptions about future trends. In particular the impact of spatial correlations between time series (typically for wind and solar resources) has been investigated over a test case leading to the main conclusion that the reliability of the system can be overestimated when spatial correlations are neglected (see article *“The importance of spatial correlations in Monte Carlo adequacy simulations”*). These TS are used to perform power flow simulations (system adequacy with an hourly time step): for each scenario (generation mix and demand profile), each time horizon and each Monte Carlo year, the adequacy simulator returns the time series of generation and consumption, as well as the availability of each thermal unit and the system cost.

The initial pan-European grid (around 8000 nodes) is first reduced to obtain a simplified nodal grid of around 1000 nodes (it is not relevant to keep the full network for long-term studies). To that purpose, a new clustering approach for a large transmission network has been developed. The clustering algorithm relies on a combination of classical clustering techniques based on k-means algorithm [9] and a heuristic algorithm which keeps the active transmission devices such as Phase-Shifting Transformers (PST), High-Voltage Direct Current (HVDC) links embedded in the system in the reduced network.

Once the reduction is made, time series of load and generation produced by the adequacy simulations for each country are distributed on each node based on pre-defined distribution keys, which are calculated using the method developed in WP2 (see D2.1 “Data sets of scenarios for 2050”). This is made for all types of load and generation, and for each scenario and time horizon.

Overload problems are then detected and congestion of transmission lines in the initial grid are quantified with a DC Optimal Power Flow (DCOPF) model written in AMPL [7] and solved with FicoXpress [8]. This problem is addressed without any prior selection of representative snapshots (which would not ensure an exhaustive detection of overload problems), while using system flexibility in the most efficient way (such as costless devices (PST or HVDC links) or redispatching associated to a cost).

This 3^{rd} step is based on the identification of critical branches, defined as the transmission lines that present a special interest for the purposes of transmission expansion planning (e.g. frequently congested or bringing flexibility to the system), and on a heuristic algorithm to build an initial partition based on those critical branches, which is then refined by a clustering technique using the k-means algorithm. The network reduction method is described in the following article: *“*Methodology for network reduction according to critical branches: focus on network partition“. The output of step 3 is an equivalent zonal network (100 nodes) with parameters (namely, the capacities and reactances of the inter-zonal corridors) that best approximate the characteristics of the original system.

The 4^{th} step aims at providing a sequential Transmission Expansion Plan (TEP) up to 2050, with a common development of the network for all the scenarios up to 2030 (see Fig. 2 ). The expansion plan given for the zonal network (100 nodes) minimizes both the investment and the O&M costs of the transmission system: it is compared to two other architectures: the “super-grid” solution and the “local development” solution (penalization of short, respectively long distance lines).

In order to reduce both the required computing power and the computational time of the TEP optimization, it is proposed to select a subset of snapshots as representative as possible and to use it to assess the reliability and the profitability of the transmission grid. Similarly, the set of possible reinforcement options is reduced based on the assessment of their profitability [10] in a given state of the grid. This approach is described in the following article *“Methodology to develop an optimal zonal grid expansion plan considering several scenarios: focus on snapshot selection”**.*

In each scenario and for each time-horizon, the options which are the most beneficial for the system are selected, i.e. the resulting reinforcement investment and its operational costs are compared to an ideal situation of generation and costs computed in step 1 (i.e. copper plate grid which minimizes systems costs), i.e. once an investment has been selected, the operational impact of the reinforcement is modelled as the difference between the costs of operating the system with and without new reinforcement investments, which defines the profitability of an investment. The developed approach is therefore based on two optimization levels: investment and operation. The objective of the investment problem is to minimize the overall cost all along the time horizons (2020 to 2050) and for all the scenarios (weighted by their probability of occurrence), where a part of the operating cost is itself an optimization (operational level) minimizing, for a given grid and a selected set of snapshots, the deviations of generation and consumption from step 1 (adequacy without grid).

Once the three different modular development plans (super, local and optimal grids) have been established on the zonal grid (100 nodes), the resulting architectures are defined on the simplified nodal grid (1000 nodes) for the first two time horizons. They should comply with the grid capacities defined in the zonal approach and ensure (N-1) system reliability taking into account all possible flexible devices.

For each inter-zonal capacity, several candidates are selected between each pair of zones using heuristics. Then, an optimizer chooses the best configuration mixing all the candidates for all the inter-zonal capacities, ensuring reliability and fulfilling the given inter-zonal capacities.

In the final step, the robustness of the proposed nodal grid architectures for the first two time horizons is checked to ensure that these grids can be operated without major voltage or stability concerns. This analysis involves the study of voltage-reactive power control and stability, transient stability and small-signal stability.

To that purpose, an AC load flow model of the grid to account for reactive power flows and bus voltage magnitude variation is needed as well as simplified dynamic models of generators (wind generator) and other dynamic devices (e.g. VSC-HVDC) to carry out the different stability analyses.

Voltage-reactive power analyses (reactive power compensation and voltage control resource) ensuring the voltage stability of the power system have been carried out. Starting from the converged AC load flow, a sequential linear programming optimization algorithm determines the reactive power compensation resources and the voltage control means (generator terminal voltages and transformer taps) to reach a desired voltage profile.

The impact of the control systems of the different components on the power system performances has also been studied on a two-area system with wind generators and one HVDC link (LCC and VSC technologies). This use case has shown that control systems of wind generators and HVDC links have a great impact on the critical clearing time, and thus on the power system performances.

The present long-term planning methodology has been tested on the current French-Spanish transmission systems (2196 nodes and 3715 transmission lines). The initial grid was not reduced since its size was close to the 1000 nodes (cf. step 2). Then, starting from the 2012 installed capacities in both countries, 2 different scenarios for 3 time horizons (2030, 2040, 2050) were developed. The first scenario keeps the same energy mix as 2012 (with different installed capacities), while the second has an increased share of renewable energy sources: 10 Monte-Carlo years have been generated per scenario and time horizon. The power system includes around 300 thermal units.

The computational times needed for the adequacy and DCOPFs simulations over one year using FicoXpress [8] are presented in Table 1. This gives an estimation of the resources that would be needed for a larger study. As a consequence, a simulation run on 160 cores (10 times the CPU capacity used for the current case study) for 2000 Monte Carlo years, 7 different scenarios and 6 time horizons, could then last around 400 days and generate 500 TB of output data to be stored.

This work constitutes the core component of the enhanced network expansion planning methodology of the e-Highway-2050 project, supported by the EU Seventh Framework Programme and is connected to the following e-Highway2050 knowledge articles:

- e-Highway: Challenging energy scenarios for the pan European transmission system by 2050
- e-Highway 2050: Approach towards a European cluster model
- e-Highway 2050: Methodology for 2050 scenario quantification

A series of specific highlights on particular aspects of the method is available in the following articles:

- e-Highway: The importance of spatial correlations in Monte Carlo adequacy simulations
- e-Highway: Methodology for network reduction according to critical branches: focus on network partition
- e-Highway: Methodology to develop an optimal zonal grid expansion plan considering several scenarios: focus on snapshot selection

[1] Y. Li, and J.D. McCalley, "Design of A High Capacity Inter-Regional Transmission Overlay for the U.S.," *IEEE Trans. Power Systems*, vol. PP, pp. 1-9, Jun. 2014.

[2] F.D. Munoz, B.F. Hobbs, and S. Kasina, "Efficient proactive transmission planning to accommodate renewables," in *2012 IEEE Power and Energy Society General Meeting*, pp. 1-7.

[3] D.C. Hill, D. McMillan, K.R.W. Bell, and D. Inflied, "Application of Auto-regressive Models to UK Wind Speed Data for Power System Impact Studies,"* IEEE Trans. Sustainable Energy*, vol.3, pp. 134-141, Jan. 2012.

[4] M. Doquet, "Use of a stochastic process to sample wind power curves in planning studies," in *Power Tech 2007 IEEE Lausanne Conf.*, pp.663-670.

[5] *Generation Adequacy Report 2012*, RTE, Paris, France. [Online]. Available: http://www.rte-france.com/uploads/Mediatheque_docs/vie_ systeme/annuelles/bilan_previsionnel/an/generation_adequacy_report_2012.pdf

[6] G. Morales-España, J.M. Latorre, and A. Ramos, "Tight and Compact MILP Formulation of the Thermal Unit Commitment Problem," *IEEE Trans. Power Systems*, vol. 28, pp. 4897-4908, Nov.2013.

[7] *AMPL Optimization*, http://ampl.com.

[8] FICO Xpress Optimization Suite, *FICO*, http://www.fico.com/en/ products/fico-xpress-optimization-suite/.

[9] N. Shi, Liu X., and Y. Guan, "Research on k-means Clustering Algorithm: An Improved k-means Clustering Algorithm, *"** 2010 Third International Symposium Conf. on Intelligent Information Technology and Security Informatics (IITSI)*, pp. 63-67.

[10] S. Lumbreras, A. Ramos, and P. Sánchez, "Automatic selection of candidate investments for Transmission Expansion Planning," *International Journal of Electrical Power & Energy Systems*, vol. 59, pp. 130–140, Jul. 2014

[11] Bahiense, L., et al., "A mixed integer disjunctive model for transmission network expansion," *IEEE Trans. Power Systems*, vol. 16, pp. 560-565, Aug. 2001.

**Camille Pache, RTE,**France, e-mail: camille.pache@rte-france.com**Baptiste Seguinot,****RTE,**France, e-mail: baptiste.seguinot@rte-france.com**Alessandro Zani,****RSE,**Italy, e-mail: alessandro.zani@rse-web.it**Sara Lumbreras,**Universidad Pontificia Comillas, Spain, e-mail: sara.lumbreras@iit.upcomillas.es**Andrés Ramos,**Universidad Pontificia Comillas, Spain, e-mail: andre.ramos@iit.upcomillas.es**Luis Rouco,**Universidad Pontificia Comillas, Spain, e-mail: luis.rouco@iit.upcomillas.es**P. Panciatici, RTE**, France, e-mail: patrick.panciatici@rte-france.com**Jean Maeght,****RTE**, e-mail: jean.maeght@rte-france.com**Sergeï Agapoff,****RTE**, e-mail: sergei.agapoff@rte-france.com**Leif Warland**,**SINTEF Energy,**Norway, email: leif.warland@sintef.no

**Gerald Sanchis, RTE,**e-mail: gerald.sanchis@rte-france.com**Nathalie Grisey, RTE**e-mail: nathalie.grisey@rtefrance.com